Equipped with this new distance, we derive an efficient approximation for the graph alignment problem, which is a necessary step in graph comparison. Our approximation permits to remove computational complexity bottlenecks in the alignment problem (e.g., [1]}). It also enables the comparison of graphs of different size, which brings an important advantage in practice. The solution of the graph alignment problem directly leads to the computation of the minimal filter graph distance, which eventually permits to compare different graphs.
